Question

How do you differentiate `f(x)=(-e^x+secx)(3x^2-2x)` using the product rule?

Answer 1

`f'(x)=(-e^x+secxtanx)(3x^2-2x)+(-e^x+secx)(6x-2)`

Explanation:

`f(x)=(-e^x+secx)(3x^2-2x)=g(x)h(x)`
`f'(x)=g'(x)h(x)+h'(x)g(x)`

`g(x)=-e^x+secx`
`g'(x)=-e^x+secxtanx`

`h(x)=3x^2-2x`
`h'(x)=6x-2`

`f'(x)=(-e^x+secxtanx)(3x^2-2x)+(-e^x+secx)(6x-2)`